令S=2^99+2^98+2^97+.+2+12S=2^100+2^99+2^98+2^97+.+2^2+22S-S=2^100-1S=2^100-1即2^99+2^98+2^97+.+2+1=2^100-1
设S=2的99次方+2的98次方+2的97次方+···+2+1两边同x22S=2的100次方+2的99次方+2的98次方+2的97次方+···+22S-S=S=2的100次方-1
